On the efficiency of Bertrand and Cournot equilibria with product differentiation

Vives, Xavier

doi:10.1017/cbo9780511528231.015

Cited by 89 publications

(132 citation statements)

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“…With Bertrand competition residual demand is more sensitive to changes in price thereby yielding lower equilibrium prices (Martin 2002). Zanchettin (2006) shows that this result extends to duopolies with exogenous cost differences while for symmetric cost structures the result also extends to an oligopoly (Vives 1985). Häckner (2000) reveals however that in an oligopoly of complementary goods with exogenous quality differences the low-quality firms may charge higher prices under Bertrand competition than under Cournot competition.…”

Section: Introductionmentioning

confidence: 89%

Dynamic efficiency of Cournot and Bertrand competition: input versus output spillovers

Hinloopen

Vandekerckhove

2009

J Econ

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We consider the efficiency of Cournot and Bertrand equilibria in a duopoly with substitutable goods where firms invest in process R&D that generates input spillovers. Under Cournot competition firms always invest more in R&D than under Bertrand competition. More importantly, Cournot competition yields lower prices than Bertrand competition when the R&D production process is efficient, when spillovers are substantial, and when goods are not too differentiated. The range of cases for which total surplus under Cournot competition exceeds that under Bertrand competition is even larger as competition over quantities always yields the largest producers' surplus.

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Section: Introductionmentioning

confidence: 89%

Dynamic efficiency of Cournot and Bertrand competition: input versus output spillovers

Hinloopen

Vandekerckhove

2009

J Econ

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“…duopoly with substitute goods and product R&D. Vives (1985) and Singh and Vives (1984) found that Bertrand competition results in higher consumer surplus, lower profits and higher overall welfare than Cournot competition in a duopoly model where goods are substitutes and the firms' only choice variable is either price or output. Motta (1993) found price competition to result in higher consumer surplus, profits and overall welfare than quantity competition in the context of a vertically differentiated duopoly with either fixed or variable costs of quality improvement.…”

Section: This Paper Compares Bertrand and Cournot Equilibria In A Difmentioning

confidence: 99%

“…Note that (1) is a quality-augmented version of the standard quadratic utility function used, among others, by Singh and Vives (1984), Vives (1985), and Qiu (1997). Thus x i and u i are, respectively, the quantity and quality of variety i and…”

Section: The Modelmentioning

confidence: 99%

Comparing Cournot and Bertrand equilibria in a differentiated duopoly with product R&D

Symeonidis

2003

International Journal of Industrial Organization

159

108

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This paper compares Bertrand and Cournot equilibria in a differentiated duopoly with substitute goods and product R&D. I find that R&D expenditure, prices and firms' net profits are always higher under quantity competition than under price competition. Furthermore, output, consumer surplus and total welfare are higher in the Bertrand equilibrium than in the Cournot equilibrium if either R&D spillovers are weak or products are sufficiently differentiated. If R&D spillovers are strong and products are not too differentiated, then output, consumer surplus and total welfare are lower in the Bertrand case than in the Cournot case. Thus a key finding of the paper is that there are circumstances where quantity competition can be more beneficial than price competition both for consumers and for firms.

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“…We allow for the possibility that i U is not additively separable, like the quadratic quasi-linear utility function used by Vives (1985) and Ottaviano et al (2002). 33 Finally, each consumer has an initial endowment of the numéraire, 0…”

Section: The Modelmentioning

confidence: 99%

The Henry George Theorem in a second-best world

Behrens

Kanemoto

Murata

2015

Journal of Urban Economics

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The Henry George Theorem (HGT) states that, in first-best economies, the fiscal surplus of a city government that finances the Pigouvian subsidies for agglomeration externalities and the costs of local public goods by a 100% tax on land is zero at optimal city sizes. We extend the HGT to distorted economies where product differentiation and increasing returns are the sources of agglomeration economies and city governments levy property taxes. Without relying on specific functional forms, we derive a second-best HGT that relates the fiscal surplus to the excess burden expressed as an extended Harberger formula.

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On the efficiency of Bertrand and Cournot equilibria with product differentiation

Cited by 89 publications

References 0 publications

Dynamic efficiency of Cournot and Bertrand competition: input versus output spillovers

Dynamic efficiency of Cournot and Bertrand competition: input versus output spillovers

Comparing Cournot and Bertrand equilibria in a differentiated duopoly with product R&D

The Henry George Theorem in a second-best world

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